Back in Argentina there were knowing smiles and the sense of it all being perfectly usual. "Tremendo Debut" ran the headline in El Diario. El Intransigente went for "El 'Kun' Brillo" while Olé hailed "Ciudadano Ilustre" (the Illustrious Citizen), reflecting on the night when Sergio Agüero announced his arrival in English football and offered the first hard evidence that Carlos Tevez may no longer be as essential to Manchester City as water is to a flower.

As debuts go, City have to go back a long way to find anything on a similar level to what was witnessed under the floodlights against Swansea City on Monday, culminating in that almost brutal, spearing drive from a distance where only a certain type of footballer would have thought it feasible to score.

Ali Benarbia was probably the last City player whose debut invited such a frisson of excitement, even if that was back in the days when the stands at Maine Road too often rang with groans and moans. Denis Law scored on both his debuts for the club and City supporters still recall the body-swerve with which Georgi Kinkladze eluded three opponents 15 seconds into his first match. But it is probably necessary to go back to 5 September 1981 to find the nearest comparison: Trevor Francis's first appearance, with a massed Mancunian following behind one of the goals at Stoke's Victoria Ground. Francis, like Agüero, scored twice and set up the third. "City have a new hero", the Guardian reported the following day.

Too much can be read into one game, of course. Footballers, like managers, can have honeymoon periods only for the sun to dip. Agüero, however, looks like a man in a hurry and for his new employer, the Argentinian's presence could conceivably go a long way to shifting the perception that has built of Roberto Mancini's team being too conservative to take the Premier League trophy from one side of Manchester to the other.

The allegation is not entirely justified but Mancini made the point himself a couple of weeks ago, that the team would have to conjure up an extra 10 to 15 goals. They managed 60 last season, which is not too shabby but still a fair distance behind Manchester United (78), Arsenal (72) and Chelsea (69), and the memories linger of those occasions – predominantly the home fixture against United and away at Arsenal – when a scoreless draw felt like the sum total of their ambitions.

That is not to suggest Mancini will change his philosophy that the first rule of a football match is not to concede, but the difference this season is that his options in attack have improved and, in turn, there no longer appears to be the same over-reliance on Tevez.

What should not be overlooked from Monday's 4-0 rout either was the fact that Edin Dzeko no longer looked like the striker who made fans wince at times last season. The Bosnian was sharp, sure of touch and played with an assurance that was rarely seen last time. He, too, will be subjected to the small print of Agüero's opening statement that it was "only Swansea" but the early signs are of someone who has rediscovered the self-belief that made him such a prolific scorer in the Bundesliga.

Then there is the fact that Tevez looks almost certain to stay at City, with Mancini reiterating there were no potential buyers and that last season's joint winner of the golden boot could return against Bolton Wanderers on Sunday. Tevez was not ready against Swansea, essentially because he decided against coming back from a post-Copa América break at the same time as Agüero and Pablo Zabaleta, his Argentina team-mates.

He did not bother gracing the Etihad Stadium with his presence on Monday either, and has stretched everyone's patience to the point that Mancini must surely remove the captaincy. Tevez, though, is still a striker who could be of significant use and, perhaps crucially, someone who can play well, sometimes brilliantly, regardless of whatever grievances are clattering around in his brain.

A Tevez-Agüero partnership has the potential to trouble the most accomplished defence, even before we consider the possible permutations with Dzeko, the brilliance of David Silva behind them, Adam Johnson's penetration from wide and the prospect that this is the time for Mario Balotelli to develop into a serious footballer. Trying to predict what will happen with the Italian is not easy, especially as he is still troubled by knee issues, but the fact he scored 10 times in 29 appearances last season – a campaign he regards as a personal failure – demonstrates he can have a significant input.

For Mancini, there is also the prospect of Samir Nasri adding his refined touches and Agüero – "a photocopy of Romario", to use the manager's description – getting even better once he is fitter and more attuned to English football.

The artillery is definitely there, which makes it really a question of what Mancini does with it. In the Community Shield he reacted to United making it 2-2, from 2-0 down, by taking off Balotelli and bringing on Gareth Barry, a holding midfielder, for the final 30 minutes. Balotelli, in fairness, had been poor in the extreme but it is difficult to imagine Sir Alex Ferguson making that kind of change. This, perhaps, is the time Mancini looks at the goalscorers and creators in his squad and knows he can take off the handbrake.